Superconductivity in graphene stacks: From the bilayer to graphite

We study a possible superconducting phase transition, both in a graphene bilayer and in graphite, by assuming an on-site attractive interaction between the electrons. We consider a stack of graphene layers with hopping between adjacent sheets, derive an expression for the free-energy (effective potential) of this system and determine the superconducting critical temperature as a function of the chemical potential. This presents a dome-shaped curve characteristic of several layered materials. We show that the hopping between adjacent layers increases the critical temperature ( T c ) for small values of the chemical potential ( μ ) and produces a finite Tc at μ = 0 . Physically, this can be ascribed to the formation of a Fermi surface for a finite interlayer hopping. We then extend our results to a minimal model for graphite and show that the transition temperature is higher than that for the graphene bilayer for small values of chemical potential. This might explain why intrinsic superconductivity is observed in graphite.